Social security, tax benefits, death benefits (including child custody), health insurance coverage, legal (marital communications privilege) There are probably thousands of these baked into our state and federal laws.
There are a ton of legal ramifications, including tax benefits (it's advantageous for a married couple to file income taxes jointly), immigration (spousal visas etc.), inheritance, and so on.
I believe immigration and federal taxes, which are handled solely by the federal government, are not affected as the US (on a national level) already recognized same-sex marriages after the DOMA overrule.
I don't know all (or many) of the specifics but I know a big one is that in certain states/situations partners were not guaranteed visitation rights in the hospital on the grounds that they weren't legally married.
I think estate planning and inheritance all could have been done before (you can leave your money/assets to whoever). This just ensures your spouse gets it even if you don't have a will.
From what I understand, in some cases where the couple didn't do any estate planning the deceased partner's family could seize the deceased partner's property out of spite, sometimes leaving the surviving partner homeless or destitute.
I understand the social consequences. But what legal rights have been granted now that did not exist previously ?